Given: The figure:
Required: Area of the figure.
Explanation:
Observe the figure carefully.
It has one square with side 50+50 = 100 units.
It has four partial circles, with radius 50 units.
Area of the figure is
Area of 1 square + The area of four partial circles.
Now, area of square with side 100 units is
[tex]\begin{gathered} A_1=(100)^2 \\ A_1=10000 \end{gathered}[/tex]Now, the circles are not complete, they are partial. Since the angle is shown to be right angles, so 90/360, that is 1/4 th of the circle is not there. So we have to calculate area of 3/4 th circle only.
Now, area of 4 (3/4)th circles is
[tex]\begin{gathered} A_2=4\times\frac{3}{4}\times\pi\times r^2 \\ A_2=4\times\frac{3}{4}\times3.1416\times50^2 \end{gathered}[/tex]Calculating
[tex]\begin{gathered} A_2=3\times3.1416\times2500 \\ A_2=23562 \end{gathered}[/tex]So total area
[tex]\begin{gathered} A=A_1+A_2 \\ A=10000+23562=33562\text{ square units} \end{gathered}[/tex]Final Answer: Option D is correct.
